Hammers co-owner David Gold revealed earlier in the week that no more additions will be sanctioned until players are moved on.
Allardyce has already spent some £25million this summer and has reached his limit in terms of squad salary.
It has been suggested that he may look to make one more move before the window closes, with West Ham still short on strikers, but Allardyce insists he is happy with what he has got and has no plans to request more cash.
He said: "I've got no money left.
"That's it. If we wanted to bring a new player in, we would have to sell some players.
"But I'm not looking to do that because I'm happy with the squad I've got.
"I'm not panicking because we've done all our business as quick as we possibly can."
Allardyce's attacking options should be bolstered over the next week or so by the return to fitness of Andy Carroll, with the England international close to shaking off a heel complaint.
"Over the next few days, I expect him to step up training," added Allardyce.